The present invention relates to methods and apparatus for controlling dynamic physical systems comprising airfoils (e.g., planes, wind turbines, helicopters). Examples of airfoils include: fixed airplane wings, moving blades of a propeller, rotor or turbine; wind turbine blades; helicopter rotor blades; gas turbine blades; water turbine blades; wings on high-performance automobiles; hydrofoils; airfoil-shaped submarine periscopes; airfoil-shaped exhaust stacks; sails on sailing ships; and power lines. More generally, the present invention relates to analysis and control of dynamic systems comprising any dynamic physical system characterized by a discontinuous hysteresis function, including highly-discontinuous functions (i.e., having greater than two discontinuities).
Researchers have been investigating limit cycle behavior for many different engineering fields. Specific applications that relate to the category of time-periodic systems include, for example, helicopter blades in forward flight, wind turbine blades generating electricity, and airplane wing flutter, all of which Limit-Cycle Oscillations (LCO's) may become present. The prediction and control of LCO behavior in a system continues to be a challenge and an on-going area of research. A limit-cycle on a plane or a two-dimensional manifold is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity, or as time approaches minus-infinity. Such behavior is exhibited in some nonlinear systems.
Several researchers are investigating cyclic methods to compute limit-cycle oscillations for potentially large, nonlinear systems of equations. For example, a harmonic balance technique can be used for modeling unsteady nonlinear flows in turbomachinery. Here, a transonic front stage rotor of a high-pressure compressor was found to flutter in torsion, but reached a stable limit cycle; demonstrating that strongly nonlinear flows can be modeled accurately with a small number of harmonics.
Our goal was to determine the range of applicability of models of varying fidelity to the numerical prediction of wing flutter LCOs, and related evaluations. A simple 1-DOF aeroelastic model of an airfoil with nonlinear structural coupling was used to demonstrate the efficacy of the general procedure.
In particular, with respect to large wind turbine systems (0.5-5 MW rated power) the dynamic stability limits of the individual blades, and of the entire assembly of 3-blades/Hub/housing/tower, are not well known. It is difficult and expensive to test a full-sized blade under the high wind loads (e.g., greater than 12 m/s) needed to induce dynamic stall, flutter, and/or instability. Because the limits of stability are not well known, existing large wind turbine farms operate conservatively, with a considerable margin of safety (both in terms of max wind speed and fatigue lifetime) as part of smart rotor technology as applied to wind turbines and rotorcraft. As the need for electric power increases, electric utilities will be pushed to operate the blades closer and closer to their stability limits to increase efficiency and extend lifetimes.